Question

The base of a triangular pyramid is a triangle with corners at `(7 ,5 )`, `(6 ,9 )`, and `(3 ,8 )`. If the pyramid has a height of `15`, what is the pyramid's volume?

Answer 1

Volume of a pyramid is `32.45` cubic unit.

Explanation:

Volume of pyramid is 1/3.base area.hight. Base area is the area of triangle ABC of sides `AB=a=sqrt((7-6)^2+(5-9)^2)=sqrt17=4.12 ; BC=b =sqrt((6-3)^2+(9-8)^2)=sqrt 10=3.16 ; CA=c=sqrt((3-7)^2+(8-5)^2)=sqrt25=5.00`

Area of the triangle `A_t=sqrt( s (s-a)(s-b)(s-c)) ;s=(a+b+c)/2 =(4.12+3.16+5)/2=6.14 :. A_t= sqrt(6.14(6.14-4.12)(6.14-3.16)(6.14-5.0))=6.49`

Volume of pyramid is `V=1/3*A_t*h= 1/3*6.49*15=32.45` cubic unit [Ans]